Section 12–6 Nuclear forces

(Interaction range / Mathematical approximation / Fundamental machinery)

In this section, Feynman discusses nuclear forces from the perspectives of interaction range, mathematical approximation, and fundamental machinery.

1. Interaction range:

“These forces have a very tiny range which is just about the same as the size of the nucleus, perhaps 10⁻¹³ centimeter (Feynman et al., 1963, section 12–6 Nuclear forces).”

Feynman concludes this chapter with a brief discussion of nuclear forces. He mentioned that there was no known law of nuclear forces. Currently, it is still challenging to accurately calculate the force between two nuclei. For instance, Wilczek (2007) writes that “[i]n principle, the equations of QCD contain all the physics of strong internucleon forces. But in practice, it is extremely difficult to solve the equations and calculate those forces (p. 156).” The physical law of nuclear forces is now known as quantum chromodynamics (QCD) and it is still true that these forces have a very tiny range which is about 10⁻¹³ centimeter (or about the size of a nucleon). One may criticize the use of the term nucleus here because it is possible to be much larger than a nucleon.

Physicists, nowadays, use the term “strong force” instead of “nuclear force.” We may estimate the range of strong force to be about the size of a nucleon because the quarks enclosed are point-like objects. Wilczek (2015) explains that “[t]he use of ‘strong’ and ‘force’ together is potentially ambiguous because ‘strong force’ could be taken to mean a powerful source of acceleration. Thus when speaking of the gravitational influence of a neutron star, or a black hole, one might say that gravity exerts a strong force on a nearby planet. To avoid ambiguity, in such cases I use terms like ‘powerful force’ or ‘powerful interaction,’ avoiding ‘strong force’ and ‘strong interaction’ (p. 389).” Strictly speaking, the concept of force is also not suitable in QCD (or quantum theory), but the concept of energy is more natural.

2. Mathematical approximation:

“Any formula that can be written for nuclear forces is a rather crude approximation which omits many complications… (Feynman et al., 1963, section 12–6 Nuclear forces).”

Feynman mentions that any formula that can be written for nuclear forces is only a crude approximation which neglects many complications. He adds that nuclear forces disappear as soon as the particles are at a great distance apart, and states that they are very strong within the 10⁻¹³ cm range. Physicists currently explain that the nuclear force is a residual effect of the strong force. In short, the strong force is relatively stronger as the quarks separate from each other, and it is weaker if the quarks approach one another. The idea that strong force becomes weaker at short distances is known as asymptotic freedom (or “charge without charge”).

According to Feynman, nuclear forces do not vary inversely as the square of the distance, but they decrease exponentially over a distance r according to the equation, F = (1/r²)exp(−r/r₀), in which the distance r₀ is of the order of 10⁻¹³ centimeter (or 10⁻¹⁵ m). Mathematically, this is incorrect because it suggests that the nuclear forces approach infinity when the distance r approaches zero. Based on experiments of the deep inelastic scattering of electrons off nucleons, physicists deduce that quarks behave like free particles in the asymptotic limit of zero separation. Interestingly, Zee (2015) explains that “[q]uarks are like some lovers: When they are far apart, they want each other, but when they are close together, they barely acknowledge (p. 205).”

3. Fundamental machinery:

“…we do not understand them in any simple way, and the whole problem of analyzing the fundamental machinery behind nuclear forces is unsolved (Feynman et al., 1963, section 12–6 Nuclear forces).”

Feynman says that the laws of nuclear force are very complex and he does not have a simple way of understanding these laws. (He mentioned initially that there was no known law of nuclear forces.) The problem of analyzing the fundamental machinery of nuclear forces was unsolved when this lecture was delivered. George Zweig, Feynman’s doctoral student, developed a model and named the fundamental particles as “aces” in 1964. Gell-Mann also proposed a quark model within the same year. In a public lecture on QED, Feynman (1985) expresses that “Murray Gell-Mann nearly went crazy trying to figure out the rules by which all these particles behave, and in the early 1970s they came up with the quantum theory of strong interactions (or quantum chromodynamics), whose main actors are particles called ‘quarks’ (p. 132).”

Just like the electromagnetic force is mediated by photons, the strong force is mediated by gluons. During the public lecture on QED, Feynman (1985) explains that “[s]omething else has been invented to go back and forth and hold quarks together; something called ‘gluons’ (p. 134).” The gluons are labeled different colors (red, blue, and green) that behave like an electric charge. The color charge is conserved in the interactions of quarks such that the color of a quark is changed after absorption of a color gluon. However, Feynman (1985) responds that “[t]he idiot physicists, unable to come up with any wonderful Greek words anymore, call this type of polarization by the unfortunate name of ‘color,’ which has nothing to do with color in the normal sense (p. 136).”

Questions for discussion:

1. How would you explain the strong force is a short range force?

2. How would you justify the word “strong” as used in strong force?

3. How would you describe the fundamental machinery behind the strong force?

The moral of the lesson: we may understand the nature of strong force from the perspectives of its interaction range, relative strength, and the interactions of quarks.

References:

1. Feynman, R. P. (1985). QED: The strange theory of light and matter. Princeton: Princeton University Press.

2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

3. Wilczek, F. (2007). Particle physics: Hard-core revelations. Nature, 445(7124), 156-157.

4. Wilczek, F. (2015). A Beautiful Question: Finding Nature’s Deep Design. New York: Penguin Press.

5. Zee, A. (2015). Fearful Symmetry: The Search for Beauty in Modern Physics. Princeton, NJ: Princeton University Press.